# 8. Permutations and the determinant

There are many operations that can be applied to a square matrix. This chapter is devoted to one particularly important operation called the **determinant**. In effect, the determinant can be thought of as a single number that is used to check for many of the different properties that a matrix might possess. In order to define the determinant operation, we will ﬁrst need to define permutations.

### Contributors

- Isaiah Lankham, Mathematics Department at UC Davis
- Bruno Nachtergaele, Mathematics Department at UC Davis
- Anne Schilling, Mathematics Department at UC Davis

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